Abstract
In this paper, we propose a new arc-search predictor-corrector infeasible-interior-point algorithm for linear complementarity problems over symmetric cones with the Cartesian P∗(κ)-property (P∗(κ)-SCLCP). The proposed algorithm is based on a wide neighborhood of the central path and searches the optimizers along the ellipses that approximate the entire the central path. The algorithm uses a commutative class of search directions, which includes the Nesterov-Todd direction and the xs and sx directions. To the best of our knowledge, this is using a new strategy in the complexity analysis; we improve the theoretical complexity bound of an arc-search infeasible-interior-point method for P∗(κ)-SCLCP. Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm.
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Funding
The research of the authors were in part supported by a grant from INSF (No. 96008721). The authors were also partially supported by Department of Mathematics, Yazd University, Yazd, Iran.
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Shahraki, M.S., Delavarkhalafi, A. An arc-search predictor-corrector infeasible-interior-point algorithm for P∗(κ)-SCLCPs. Numer Algor 83, 1555–1575 (2020). https://doi.org/10.1007/s11075-019-00736-4
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DOI: https://doi.org/10.1007/s11075-019-00736-4